Is semi-implicit Euler unconditionally stable?

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lgchemer
Posts: 5
Joined: Fri Jan 20, 2012 11:28 pm
Location: Urbana, IL

Is semi-implicit Euler unconditionally stable?

Post by lgchemer »

Hello.

I just wonder if the (widely used) semi-implicit Euler time integration is "unconditionally stable."
My intuition says "no" because the gravity is explicitly integrated.
However, I see the simulation is very stable with increase of time step size (although inaccuracy certainly increases).

Is there any one know if it is unconditionally stable or not.
If not, is there any theoretical numerical limit such that the stability is guaranteed?

Thanks much!!
RandyGaul
Posts: 43
Joined: Mon May 20, 2013 8:01 am
Location: Redmond, WA

Re: Is semi-implicit Euler unconditionally stable?

Post by RandyGaul »

It is not, however it is "good enough" as per Erin Catto: integration slides; information about implicit, forward and semi-implicit.

Stability will lower at very low framerates, as the approximation error will be larger and larger.
bone
Posts: 231
Joined: Tue Feb 20, 2007 4:56 pm

Re: Is semi-implicit Euler unconditionally stable?

Post by bone »

It depends on what you're simulating. For a simple mass-spring system, there is a simple formula for whether it is too stiff for semi-implicit Euler to be stable. IIRC, the oscillation frequency has to be less than half of the physics sampling frequency.
lgchemer
Posts: 5
Joined: Fri Jan 20, 2012 11:28 pm
Location: Urbana, IL

Re: Is semi-implicit Euler unconditionally stable?

Post by lgchemer »

Thanks much for your replies.
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